This is a presentation related to quantum weak measurement,where we try to describe to develop the concept of weak measurement and show how the values are different from projective measurement.
WEAK MEASUREMENT
WEAK MEASUREMENTWeak values by sequential measurementPresented
by:Sushovan Mondal(BS-MS Dual Degree,IISER KOLKATA)Supervisor:Dr.
Asoka Biswas(Dept. of Physics,IIT ROPAR) July 2015 INTRODUCTIONIn
quantum information, measurement is a very important factor.In
general measurement means to jump a quantum state into an
eigenstate of dynamical variable that is being measured.In weak
measurement the system will not collapse in one eigenstate but the
entanglement between system and the device become as weak that we
can extract the information without changing of the initial
state.It is the main funda of weak measurement. Well show how does
the probability of number dstribution changes for changing the
weakness of the measurement. Strong MeasurementIn general quantum
measurement indicates the strong measurement. That means when I
measure any quantum state with a device that will collapse the
state, in any of the eigenstate of the observable. Now say any
state can be denoted as ,which can be written as .Now if we measure
this state by strong measurement then the state will be collapse in
any one of the eigenstate according to probability distribution. As
the state is now transformed another state ,So we lost the
information related to it. We can say that this type of measurement
is due to system and device strong entanglement.
Properties of strong measurementWe consider the state as quantum
and device as classical state.The entanglement between system and
device will be strong.The initial quantum state collapse in an
eigenstate according to the observable.As the initial quantum state
collapse in other state, so the information related to the initial
state will be lost.Example: To measure the position of a state ,the
state should be collapsed ,So the information related to the
momentum of will be lost.
Concept of weak measurementBoth system and device are considered
as quantum state.They entangled weakly.Measured the devices quantum
state strongly , i.e collapse it one eigenstate.Average it over an
ensemble of these same measurements.The outcome is the weak value
of the observable. Post selection1st there is an initial state of
the state and weakly entangled with devices state .Then the
interaction operator of observable will be operated.Then select the
desirable states and discard other states, this process is called
post selection.Repeat the process several times and take
average.The weak value is given by ,where A is the operator of
observable .
Nature of weak valuesSo weak value is given by .Depending on
post selection may be orthogonal to .As the numerator tends to a
small value, so that the weak value tends to a higher value .As we
increase the weakness of the measurement the variance of the
observable will increase.But the information related to initial
state remain approximately intact.
Graphical representation of weak values
Plots of number distribution for various weaknessConsider as
operator(beam splitter operator).Change the weakness of measurement
and plot photon number distribution.Peak shifts to higher n and
variance increases with increase of weakness.
ConclusionHere we observe how the weak value of a observable
differs from the value of the projective measurement. So, as we
show here the distribution for the photon number we can also choose
other basis to show this weak values. And as the weak value is
obtained by weak interaction, so it is the more precise measurement
process in quantum mechanics. THANK YOU
